Seriously, *I* would find this stressful, and I flatter myself I have outgrown most of my second grade issues. I have been reading about open plan offices where lots of people are travelling or working from home on any given day and every one coming in in the morning finds their container with stuff and plonks down their notebook on whichever desk is free, and I have been thinking about how I would hate that.
I'd speak to the teacher again about your concerns. Maybe she'll budge.
Interestingly, I worked for a Japanese company. The corporate offices in Tokyo work this way. Each employee has a (nice) locker, where they store their personal items at night. Next to it is a closet area with numbered coat-hooks.
When you arrive in the morning, you put your purse / bag in the locker and take out your supplies (pencil box for most people, small calculator, etc). The seating is otherwise unassigned. It's meant to be collaborative.
I've been in that office 10 times. Even with an open plan, people go to the same position every day, sitting by the same people. If you sit in the wrong place as a guest, you are almost certainly messing up the flow in the office for those that work there daily.
The situation with the open, unassigned seating plan is so uncomfortable for most people that they've unofficially assigned seating.
